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Clone-selection and optimal rates of mutation

Published online by Cambridge University Press:  14 July 2016

Ilan Eshel
Ilan Eshel*
Affiliation:
Tel Aviv University
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Abstract

The paper employs methods of multitype branching processes to evaluate the probability of survival of mutable clones under environmental conditions which are unfavorable to the original parent of the clone. When other factors are taken to be constant, the long-term survival probability of a clone is implicitly demonstrated as a function of the intrinsic rate of mutation carried by this clone. The existence of a mutation rate which maximizes clone survival probability is shown and the effects of environmental deterioration on this optimal rate are studied. Finally, rigorous quantitative results are obtained for the classical situation of a Poisson distribution of offspring numbers. These results are then applied to the biological problem of indirect selection (Eshel (1972)).

Keywords

CLONE-SELECTIONRATE OF MUTATIONOPTIMAL RATE OF MUTATIONMODIFIER GENESOPTIMAL MODIFIER GENESMULTITYPE BRANCHING PROCESSESADAPTATIONINDIRECT ADAPTATIONEXTINCTION OF A POPULATION
Type
Research Papers
Information
Journal of Applied Probability , Volume 10 , Issue 4 , December 1973 , pp. 728 - 738
Copyright
Copyright © Applied Probability Trust 1973 

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References

[1] Nei, M. (1967) Modification of linkage intensity by natural selection. Genetics 57, 625626.Google Scholar
[2] Nei, M. (1969) Linkage modification and sex difference in recombination. Genetics 63, 681–699.CrossRefGoogle ScholarPubMed
[3] Feldman, W. M. (1972) Selection for linkage modification I: random mating populations. Theor. Pop. Biol. 3, 324–346.Google Scholar
[4] Karlin, S. and Mcgregor, J. (1973) Toward a theory of modifier genes. Theor. Pop. Biol. To appear.Google Scholar
[5] Karlin, S. and Mcgregor, J. (1972) The evolutionary development of modifier genes. Proc. Nat. Acad. Sci. U.S.A. 69, 3611–3614.CrossRefGoogle ScholarPubMed
[6] Fisher, R. A. (1958) The Genetical Theory of Natural Selection. Dover, New York.Google Scholar
[7] Eshel, I. (1973) Clone selection and the evolution of modifier genes. Theor. Pop. Biol. To appear.CrossRefGoogle Scholar
[8] Kimura, M. (1960) Optimum mutation rate and degree of dominance as determined by the principle of minimum genetic load. J. Genetics 57, 21–34.CrossRefGoogle Scholar
[9] Kimura, M. (1967) On the evolutionary adjustment of spontaneous mutation rates. Genet. Res. 9, 23–34.Google Scholar
[10] Karlin, S. and Mcgregor, J. (1968) The role of the Poisson progeny distribution in population genetics models. Math. Biosci. 2, 11–17.CrossRefGoogle Scholar
[11] Harris, T. (1963) The Theory of Branching Processes. Springer-Verlag, Berlin.Google Scholar
[12] Dwass, M. (1969) The total progeny in a branching process and a related random walk. J. Appl. Prob. 6, 682–686.CrossRefGoogle Scholar
[13] Karlin, S. (1966) A First Course in Stochastic Processes. Academic Press, New York.Google Scholar
[14] Crow, J. F. and Kimura, M. (1970) An Introduction to Population Genetics Theory. Harper and Row, New York.Google Scholar
[15] Moran, P. A. P. (1962) The Statistical Processes of Evolutionary Theory. Clarendon Press, Oxford.Google Scholar